# 25728_Assign1_Autumn 2012 | Bond Duration

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Bond Portfolio Management 25728 Autumn 2012 Assignment 1 Due Date: Monday April 23, 2012 (***Note: Due date is different to Subject Guide ***) You may use EXCEL to help you complete the assignment. Assignment Submission: Please submit a hard copy of the assignment in the Assignment Box on Level 3, D block, outside the School of Finance Offices. You will need to submit your spreadsheets using the Dropbox on UTSOnline. 1 QUESTION 1. (8 marks) A fixed-income portfolio manager is managing a por
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1  Bond Portfolio Management25728Autumn 2012Assignment 1Due Date:Monday April 23, 2012(***Note: Due date is different to Subject Guide ***)You may use EXCEL to help you complete the assignment.Assignment Submission: Please submit a hard copy of the assignment in the Assignment Box onLevel 3, D block, outside the School of Finance Offices. You will need tosubmit your spreadsheets using the Dropbox on UTSOnline.   2 QUESTION 1.   (8 marks) A fixed-income portfolio manager is managing a portfolio that is currently valued at \$5million. The manager is seeking to realize a rate of return of at least 5% annually over a6-year investment period.Three years later, spot rates are at 6% for all maturities. How much can the value of theportfolio fall at this time before the manager is forced to immunize, to be assured of achieving the minimum required return? State any assumptions you make. QUESTION 2. (12 marks)   Consider a 3 year bond with face value \$100, 000 which pays semiannual coupons at the ratesgiven in the table below.a. If the bond costs \$103, 721.54, show that the yield to maturity is 6.0384%.b. If the coupons are immediately reinvested until maturity, at the semiannuallycompounded rates (also given in the table below) show that the actual yield (HPY) of the bond is 6.0000%. Time (yrs)CouponRates(pa)Interest rates(pa) 0.5 5% 5.8%1.0 6% 5.6%1.5 7% 5.4%2.0 8% 5.2%2.5 9% 5.0%3.0 10% 4.8%  Note : the interest rate applies from the given time until maturity, thus the rate of 5.8% is thesemiannual rate which applies from 6 months time until 3 years time and so forth.c. If the three year semiannually compounded rate was 6.5%, what should the price of thebond be and what would the corresponding yield to maturity be?   3 QUESTION 3. (14 marks  ) Consider three fixed rate mortgages,  M  1  ,M  2   and  M  3 , and assume that the “fixed” rates may varyin parallel. The details of the mortgages are Mortgage Principal MaturityInterestRates M 1 \$ 600,000.00 10 years 6.00%M 2 \$ 350,000.00 5 years 5.00%M 3 \$ 250,000.00 3 years 4.75% where all interest is compounded monthly. Mortgage repayments are assumed to be monthly.  Assume that a parallel shift in interest rates is the same thing as an identical shift in each of the yields to maturity and ignore the initial cashflow (that is, ignore the fact that the mortgageereceives the initial principal) a Find the yields to maturity of the mortgages, from the bank’s point of view.b. Find the Macaulay, modified duration and convexity of the mortgages (again, from thebank’s point of view).c. If the bank wishes to hedge one 10 year mortgage against parallel shifts in the interestrates using the 5 year mortgage, how many of the 5 year mortgages does it require?How might the bank achieve this? ( Hint: you will need to set down the monthly repayments for the loan. These arethe cashflows of the mortgages). QUESTION 4. (14 marks  ) Consider the following Australian commonwealth Government given in the table below. Bond   Maturity   (Yrs)   Coupon   Rate   (%   p.a.)   Price   A   0.50   6.00   97.00   B   1.00   8.00   101.00   C   1.50   7.00   99.00     4 a.   Construct combinations, or portfolios of these securities that replicate the cash flow of zeros with maturities of 0.5, 1.0, and 1.5 years.b.   Use the synthetic zero to compute their prices.c.   Use the price of zeros to compute the first three discount factors and spotrates. Plot the discount factors and the spot rates. QUESTION 5. (15 marks  ) Consider the following four bonds: Bond Maturity (Yrs) Coupon Rate (%) YTM (%)Bond 1 2 5.75 5.50 Bond 2 5 6.5 6.30 Bond 3 10 6.75 6.85 Bond 4 20 7.5 7.30  Assume: Annual compounding and that bond coupons are paid annually. a.   Compute the price and the modified duration of each bond.b.   Assume the YTM of each bond decrease instantaneously by 0.2%. Compute the exactnew price of each bond, the price approximation using the duration rule and thedifference between these two prices.c.   Same question as (b) if the YTM of each bond decrease instantaneously by 1.0%.Conclude.d.   For bond 4, plot the difference between the two prices depending on the YTM change.e.   Compute the convexity of each bond.f.   Assume the YTM of each bond decrease instantaneously by 1.0%. Compute the priceapproximation using the bonds’ duration and convexity. Compare the results with theexact prices.
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